library(googlesheets4) # read google sheets
library(tidyverse) # data wrangling, grammar, and manipulation
library(ggridges) # Density Plots
library(ggprism) # plots aesthetics
library(ggpubr) # plots aesthetics
library(table1) # Table 1
library(kableExtra) # Tables
library(rstatix) # Normality tests
library(lme4) # Linear Mixed Models
library(lmerTest)
library(stargazer) #lmer and glmer mods tables
library(sjPlot) #for plotting and tableslmer and glmer mods
library(performance) # model performance and model comparison
library(flexplot)# estimates
library("sciRmdTheme") # rmarkdown theme
library(plotly)
library(irr) #ICC of JH
sheet_url <- "https://docs.google.com/spreadsheets/d/1K_IxFkSIEeZF_idOxfCg7bdBrHA0q7JNbvxf0rYosvE/edit#gid=0"
biodex_data <- read_sheet(sheet_url, sheet = "Biodex Data")
jump_data <- read_sheet(sheet_url, sheet = "Jump Data")
biodex_data$Group <- factor(biodex_data$Group, levels = sort(unique(biodex_data$Group)))
biodex_data$ID <- as.factor(biodex_data$ID)
jump_data$Group <- factor(jump_data$Group, levels = sort(unique(jump_data$Group)))
jump_data$ID <- as.factor(jump_data$ID)
jump_data <- jump_data %>% mutate(JH_cm = JH * 100)
jump_data <- jump_data %>% mutate(Depth = abs(Depth))
jump_data <- jump_data %>% mutate(Depth_cm = Depth * 100)
biodex_data$Order <- 1
jump_data$Order <- 2
Df <- bind_rows(biodex_data, jump_data)
Df_long <- Df %>% select("Subject", "ID", "Age", "Height", "Weight","Bmi","BF", "Period","Group","JH","PT_E_R_B")
biodex_data %>%
ggplot(aes(x=PTBW_E_R_B)) +
geom_density(fill="blue", alpha=0.5) +
ggtitle("Density of Age") +
xlab("Peak Torque Extension (NM/BW") +
ylab("Density") + theme_prism() + facet_grid(~Period)
biodex_data %>% group_by(Period, Group) %>% shapiro_test(PTBW_E_R_B)
## # A tibble: 18 × 5
## Period Group variable statistic p
## <chr> <fct> <chr> <dbl> <dbl>
## 1 Baseline trained PTBW_E_R_B 0.914 0.384
## 2 Baseline untrained PTBW_E_R_B 0.923 0.454
## 3 DY AG trained PTBW_E_R_B 0.941 0.619
## 4 DY AG untrained PTBW_E_R_B 0.882 0.196
## 5 DY AG ANT trained PTBW_E_R_B 0.891 0.238
## 6 DY AG ANT untrained PTBW_E_R_B 0.854 0.104
## 7 DY AG ST ANT trained PTBW_E_R_B 0.908 0.341
## 8 DY AG ST ANT untrained PTBW_E_R_B 0.911 0.358
## 9 DY ANT trained PTBW_E_R_B 0.882 0.197
## 10 DY ANT untrained PTBW_E_R_B 0.952 0.736
## 11 ST AG trained PTBW_E_R_B 0.968 0.883
## 12 ST AG untrained PTBW_E_R_B 0.938 0.593
## 13 ST AG ANT trained PTBW_E_R_B 0.986 0.986
## 14 ST AG ANT untrained PTBW_E_R_B 0.942 0.630
## 15 ST AG DY ANT trained PTBW_E_R_B 0.975 0.933
## 16 ST AG DY ANT untrained PTBW_E_R_B 0.968 0.881
## 17 ST ANT trained PTBW_E_R_B 0.964 0.849
## 18 ST ANT untrained PTBW_E_R_B 0.968 0.886
jump_data %>%
ggplot(aes(x=JH )) +
geom_density(fill="red", alpha=0.5) +
ggtitle("Density of Height") +
xlab("Jump Height (m)") +
ylab("Density") + theme_prism()+ facet_grid(~Period)
jump_data %>% group_by(Period, Group) %>% shapiro_test(JH)
## # A tibble: 18 × 5
## Period Group variable statistic p
## <chr> <fct> <chr> <dbl> <dbl>
## 1 Baseline Trained JH 0.881 0.191
## 2 Baseline Untrained JH 0.932 0.533
## 3 DY AG Trained JH 0.939 0.600
## 4 DY AG Untrained JH 0.928 0.495
## 5 DY AG ANT Trained JH 0.919 0.423
## 6 DY AG ANT Untrained JH 0.941 0.620
## 7 DY AG ST ANT Trained JH 0.866 0.137
## 8 DY AG ST ANT Untrained JH 0.963 0.837
## 9 DY ANT Trained JH 0.933 0.547
## 10 DY ANT Untrained JH 0.959 0.804
## 11 ST AG Trained JH 0.913 0.375
## 12 ST AG Untrained JH 0.903 0.308
## 13 ST AG ANT Trained JH 0.967 0.877
## 14 ST AG ANT Untrained JH 0.814 0.0408
## 15 ST AG DY ANT Trained JH 0.807 0.0339
## 16 ST AG DY ANT Untrained JH 0.873 0.161
## 17 ST ANT Trained JH 0.970 0.898
## 18 ST ANT Untrained JH 0.973 0.921
jump_data %>%
ggplot(aes(x=RSI_mod )) +
geom_density(fill="green", alpha=0.5) +
ggtitle("Density of Height") +
xlab("RSI modified") +
ylab("Density") + theme_prism()+ facet_grid(~Period)
jump_data %>% group_by(Period, Group) %>% shapiro_test(RSI_mod)
## # A tibble: 18 × 5
## Period Group variable statistic p
## <chr> <fct> <chr> <dbl> <dbl>
## 1 Baseline Trained RSI_mod 0.880 0.187
## 2 Baseline Untrained RSI_mod 0.919 0.425
## 3 DY AG Trained RSI_mod 0.965 0.860
## 4 DY AG Untrained RSI_mod 0.981 0.966
## 5 DY AG ANT Trained RSI_mod 0.922 0.444
## 6 DY AG ANT Untrained RSI_mod 0.933 0.547
## 7 DY AG ST ANT Trained RSI_mod 0.959 0.802
## 8 DY AG ST ANT Untrained RSI_mod 0.938 0.592
## 9 DY ANT Trained RSI_mod 0.720 0.00382
## 10 DY ANT Untrained RSI_mod 0.853 0.103
## 11 ST AG Trained RSI_mod 0.940 0.612
## 12 ST AG Untrained RSI_mod 0.944 0.647
## 13 ST AG ANT Trained RSI_mod 0.954 0.753
## 14 ST AG ANT Untrained RSI_mod 0.890 0.232
## 15 ST AG DY ANT Trained RSI_mod 0.884 0.204
## 16 ST AG DY ANT Untrained RSI_mod 0.896 0.268
## 17 ST ANT Trained RSI_mod 0.889 0.228
## 18 ST ANT Untrained RSI_mod 0.906 0.324
ICC_JH <- jump_data %>% select(JH_1,JH_2,JH_3,JH_4,JH_5)
icc(ICC_JH, model = "twoway",
type = "consistency", unit = "average" )
## Average Score Intraclass Correlation
##
## Model: twoway
## Type : consistency
##
## Subjects = 105
## Raters = 5
## ICC(C,5) = 0.908
##
## F-Test, H0: r0 = 0 ; H1: r0 > 0
## F(104,416) = 10.8 , p = 1.68e-71
##
## 95%-Confidence Interval for ICC Population Values:
## 0.877 < ICC < 0.933
Demographics <- biodex_data %>%
group_by(ID) %>%
slice(1) %>%
ungroup() %>% select(Group,Age,Height,Weight,Bmi,BF)
table1(~Age + Height + Weight + Bmi + BF | Group, data = Demographics)
| trained (N=8) |
untrained (N=8) |
Overall (N=16) |
|
|---|---|---|---|
| Age | |||
| Mean (SD) | 23.8 (2.87) | 25.8 (3.24) | 24.8 (3.13) |
| Median [Min, Max] | 22.5 [22.0, 30.0] | 25.5 [22.0, 30.0] | 23.5 [22.0, 30.0] |
| Height | |||
| Mean (SD) | 1.73 (0.0792) | 1.75 (0.0969) | 1.74 (0.0861) |
| Median [Min, Max] | 1.71 [1.64, 1.85] | 1.75 [1.64, 1.87] | 1.71 [1.64, 1.87] |
| Weight | |||
| Mean (SD) | 83.6 (17.5) | 87.4 (21.1) | 85.5 (18.8) |
| Median [Min, Max] | 79.7 [64.6, 117] | 86.6 [61.0, 115] | 82.3 [61.0, 117] |
| Bmi | |||
| Mean (SD) | 27.7 (3.72) | 28.2 (4.05) | 28.0 (3.76) |
| Median [Min, Max] | 27.7 [22.6, 34.1] | 28.5 [22.5, 32.7] | 28.0 [22.5, 34.1] |
| BF | |||
| Mean (SD) | 24.3 (6.71) | 26.5 (5.89) | 25.4 (6.21) |
| Median [Min, Max] | 25.5 [14.4, 33.0] | 24.4 [20.4, 35.3] | 24.4 [14.4, 35.3] |
PKET_Group_MODEL <- lmer(PTBW_E_R_B ~ Group * Period + (1 | ID), data = biodex_data)
summary(PKET_Group_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PTBW_E_R_B ~ Group * Period + (1 | ID)
## Data: biodex_data
##
## REML criterion at convergence: 1349
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.5712 -0.3890 0.0601 0.4913 3.3912
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 2492 49.92
## Residual 1420 37.68
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 252.537 22.112 29.668 11.421 2.21e-12
## Groupuntrained -38.000 31.271 29.668 -1.215 0.23388
## PeriodDY AG 30.800 18.839 112.000 1.635 0.10487
## PeriodDY AG ANT 23.350 18.839 112.000 1.239 0.21777
## PeriodDY AG ST ANT 34.963 18.839 112.000 1.856 0.06610
## PeriodDY ANT 11.725 18.839 112.000 0.622 0.53495
## PeriodST AG -2.725 18.839 112.000 -0.145 0.88525
## PeriodST AG ANT 8.475 18.839 112.000 0.450 0.65368
## PeriodST AG DY ANT -25.662 18.839 112.000 -1.362 0.17586
## PeriodST ANT 15.400 18.839 112.000 0.817 0.41540
## Groupuntrained:PeriodDY AG 10.837 26.642 112.000 0.407 0.68495
## Groupuntrained:PeriodDY AG ANT 37.550 26.642 112.000 1.409 0.16148
## Groupuntrained:PeriodDY AG ST ANT 33.462 26.642 112.000 1.256 0.21173
## Groupuntrained:PeriodDY ANT 30.325 26.642 112.000 1.138 0.25745
## Groupuntrained:PeriodST AG 13.750 26.642 112.000 0.516 0.60680
## Groupuntrained:PeriodST AG ANT 21.487 26.642 112.000 0.807 0.42165
## Groupuntrained:PeriodST AG DY ANT 89.900 26.642 112.000 3.374 0.00102
## Groupuntrained:PeriodST ANT 35.412 26.642 112.000 1.329 0.18649
##
## (Intercept) ***
## Groupuntrained
## PeriodDY AG
## PeriodDY AG ANT
## PeriodDY AG ST ANT .
## PeriodDY ANT
## PeriodST AG
## PeriodST AG ANT
## PeriodST AG DY ANT
## PeriodST ANT
## Groupuntrained:PeriodDY AG
## Groupuntrained:PeriodDY AG ANT
## Groupuntrained:PeriodDY AG ST ANT
## Groupuntrained:PeriodDY ANT
## Groupuntrained:PeriodST AG
## Groupuntrained:PeriodST AG ANT
## Groupuntrained:PeriodST AG DY ANT **
## Groupuntrained:PeriodST ANT
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation matrix not shown by default, as p = 18 > 12.
## Use print(x, correlation=TRUE) or
## vcov(x) if you need it
# AIC and BIC values
aic_val <- AIC(PKET_Group_MODEL)
bic_val <- BIC(PKET_Group_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: 1389.026
cat("BIC:", bic_val, "\n")
## BIC: 1448.422
PKET_FULL_MODEL <- lmer(PTBW_E_R_B ~ Period + Group + BF + (1 | ID),
data = biodex_data)
summary(PKET_FULL_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PTBW_E_R_B ~ Period + Group + BF + (1 | ID)
## Data: biodex_data
##
## REML criterion at convergence: 1420.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.1891 -0.4391 0.0783 0.5011 2.5139
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 2048 45.25
## Residual 1501 38.75
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 331.092 51.967 13.840 6.371 1.83e-05 ***
## PeriodDY AG 36.219 13.699 120.000 2.644 0.009290 **
## PeriodDY AG ANT 42.125 13.699 120.000 3.075 0.002606 **
## PeriodDY AG ST ANT 51.694 13.699 120.000 3.774 0.000252 ***
## PeriodDY ANT 26.887 13.699 120.000 1.963 0.051989 .
## PeriodST AG 4.150 13.699 120.000 0.303 0.762457
## PeriodST AG ANT 19.219 13.699 120.000 1.403 0.163217
## PeriodST AG DY ANT 19.288 13.699 120.000 1.408 0.161729
## PeriodST ANT 33.106 13.699 120.000 2.417 0.017167 *
## Groupuntrained 0.839 23.938 13.000 0.035 0.972574
## BF -3.858 1.992 13.000 -1.937 0.074787 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.132
## PerdDYAGANT -0.132 0.500
## PrDYAGSTANT -0.132 0.500 0.500
## PeriodDYANT -0.132 0.500 0.500 0.500
## PeriodST AG -0.132 0.500 0.500 0.500 0.500
## PerdSTAGANT -0.132 0.500 0.500 0.500 0.500 0.500
## PrSTAGDYANT -0.132 0.500 0.500 0.500 0.500 0.500 0.500
## PeriodSTANT -0.132 0.500 0.500 0.500 0.500 0.500 0.500 0.500
## Groupuntrnd -0.051 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## BF -0.931 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Grpntr
## PeriodDY AG
## PerdDYAGANT
## PrDYAGSTANT
## PeriodDYANT
## PeriodST AG
## PerdSTAGANT
## PrSTAGDYANT
## PeriodSTANT
## Groupuntrnd
## BF -0.184
# AIC and BIC values
aic_val <- AIC(PKET_FULL_MODEL)
bic_val <- BIC(PKET_FULL_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: 1446.885
cat("BIC:", bic_val, "\n")
## BIC: 1485.493
tab_model(PKET_FULL_MODEL,
collapse.ci = TRUE,
p.style = "numeric_stars", show.aic = TRUE, digits=3, digits.re = 3)
| PTBW E R B | ||
|---|---|---|
| Predictors | Estimates | p |
| (Intercept) |
331.092 *** (228.289 – 433.895) |
<0.001 |
| Period [DY AG] |
36.219 ** (9.119 – 63.318) |
0.009 |
| Period [DY AG ANT] |
42.125 ** (15.025 – 69.225) |
0.003 |
| Period [DY AG ST ANT] |
51.694 *** (24.594 – 78.793) |
<0.001 |
| Period [DY ANT] |
26.887 (-0.212 – 53.987) |
0.052 |
| Period [ST AG] |
4.150 (-22.950 – 31.250) |
0.762 |
| Period [ST AG ANT] |
19.219 (-7.881 – 46.318) |
0.163 |
| Period [ST AG DY ANT] |
19.287 (-7.812 – 46.387) |
0.162 |
| Period [ST ANT] |
33.106 * (6.007 – 60.206) |
0.017 |
| Group [untrained] |
0.839 (-46.516 – 48.194) |
0.972 |
| BF |
-3.858 (-7.799 – 0.082) |
0.055 |
| Random Effects | ||
| σ2 | 1501.281 | |
| τ00 ID | 2047.643 | |
| ICC | 0.577 | |
| N ID | 16 | |
| Observations | 144 | |
| Marginal R2 / Conditional R2 | 0.183 / 0.655 | |
| AIC | 1446.885 | |
|
||
The model diagnostics seems to show that data meets all model assumptions
check_model(PKET_FULL_MODEL)
plot_model(PKET_FULL_MODEL, title = "Peak Torque Knee Extension",
show.intercept = TRUE, show.values = TRUE, digits = 3, value.offset = 0.2) +
theme_prism()
Extract coefficients and Create predictions plots
In this plot the jitter dots are the observed values with the predicted values from the LMM in the geom_lines for each participant
model_coefs <- coef(PKET_FULL_MODEL)$ID %>%
rename(Intercept = `(Intercept)`) %>%
rownames_to_column("ID") %>%
mutate(ID = as.factor(ID))
merged_data <- left_join(biodex_data, model_coefs, by = c("ID", "BF"))
merged_data$predicted_sprint <- predict(PKET_FULL_MODEL, newdata = merged_data)
p_PTKE_ID <- ggplot(merged_data, aes(x = Period, y = PTBW_E_R_B, group = ID, color = ID)) +
geom_jitter(size=0.1) + labs(x= "Stretching Type",y="Peak Torque (Nm)",
title="Peak Knee Extension Invidual Responses") +
geom_line(aes(y = predicted_sprint)) +
theme_prism() +
theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))+
guides(color = FALSE) # This line removes the color legend for ID
## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
p_PTKE_ID
outlier <- merged_data %>% filter(ID == "6" ) %>%
ggplot(aes(x = Period, y = PTBW_E_R_B, group = ID, color = ID)) +
geom_point(size=0.1) + labs(x= "Stretching Type",y="Peak Torque (Nm)",
title="Peak Knee Extension Outlier Responses") +
geom_line() +
theme_prism() +
theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))+
guides(color = FALSE) # This line removes the color legend for ID
ggplotly(outlier)
Plot model estimates
# Predict overall estimates without considering the random effects
overall_predictions <- predict(PKET_FULL_MODEL, newdata = biodex_data, re.form = NA)
biodex_data$overall_predictions <- overall_predictions
# Aggregate the predictions
biodex_data_agg <- biodex_data %>%
group_by(Period) %>%
summarise(mean_prediction = mean(overall_predictions, na.rm = TRUE))
p_PTKE_box <- biodex_data %>%
ggboxplot(x="Period", y="PTBW_E_R_B",color="Period", add="jitter",
xlab = "Stretching Type", ylab = "Peak Torque (Nm)", title = "Peak Knee Extension") +
geom_point(data=biodex_data_agg, aes(y=mean_prediction), color="red", size=3) + # Adding the aggregated model's estimates
geom_line(data=biodex_data_agg, aes(y=mean_prediction, group=1), color="red", size=1) +
theme_prism() +
guides(color = FALSE)+
theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))
p_PTKE_box
avgKET_FULL_MODEL <- lmer(Av_PT_E_R_B ~ Period + Group + BF + (1 | ID),
data = biodex_data)
summary(avgKET_FULL_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Av_PT_E_R_B ~ Period + Group + BF + (1 | ID)
## Data: biodex_data
##
## REML criterion at convergence: 1381.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.8702 -0.5086 0.0797 0.5629 2.1822
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 772.8 27.80
## Residual 1191.2 34.51
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 122.691 33.703 14.652 3.640 0.00250 **
## PeriodDY AG 20.888 12.202 120.000 1.712 0.08953 .
## PeriodDY AG ANT 37.706 12.202 120.000 3.090 0.00249 **
## PeriodDY AG ST ANT 50.294 12.202 120.000 4.122 6.96e-05 ***
## PeriodDY ANT 23.550 12.202 120.000 1.930 0.05597 .
## PeriodST AG 13.200 12.202 120.000 1.082 0.28153
## PeriodST AG ANT 20.681 12.202 120.000 1.695 0.09270 .
## PeriodST AG DY ANT 9.431 12.202 120.000 0.773 0.44110
## PeriodST ANT 28.838 12.202 120.000 2.363 0.01972 *
## Groupuntrained -1.822 15.304 13.000 -0.119 0.90707
## BF 1.801 1.273 13.000 1.415 0.18069
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.181
## PerdDYAGANT -0.181 0.500
## PrDYAGSTANT -0.181 0.500 0.500
## PeriodDYANT -0.181 0.500 0.500 0.500
## PeriodST AG -0.181 0.500 0.500 0.500 0.500
## PerdSTAGANT -0.181 0.500 0.500 0.500 0.500 0.500
## PrSTAGDYANT -0.181 0.500 0.500 0.500 0.500 0.500 0.500
## PeriodSTANT -0.181 0.500 0.500 0.500 0.500 0.500 0.500 0.500
## Groupuntrnd -0.050 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## BF -0.918 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Grpntr
## PeriodDY AG
## PerdDYAGANT
## PrDYAGSTANT
## PeriodDYANT
## PeriodST AG
## PerdSTAGANT
## PrSTAGDYANT
## PeriodSTANT
## Groupuntrnd
## BF -0.184
# AIC and BIC values
aic_val <- AIC(avgKET_FULL_MODEL)
bic_val <- BIC(avgKET_FULL_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: 1407.49
cat("BIC:", bic_val, "\n")
## BIC: 1446.097
avgpowerKET_FULL_MODEL <- lmer(Av_Power_E_R_B ~ Period + Group + BF + (1 | ID),
data = biodex_data)
summary(avgpowerKET_FULL_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Av_Power_E_R_B ~ Period + Group + BF + (1 | ID)
## Data: biodex_data
##
## REML criterion at convergence: 1428.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2904 -0.4077 0.0631 0.4063 8.1223
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 154.3 12.42
## Residual 1937.3 44.01
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 102.6406 23.3325 20.0641 4.399 0.000275 ***
## PeriodDY AG 20.0000 15.5615 120.0000 1.285 0.201191
## PeriodDY AG ANT 33.5687 15.5615 120.0000 2.157 0.032987 *
## PeriodDY AG ST ANT 40.3125 15.5615 120.0000 2.591 0.010770 *
## PeriodDY ANT 20.9687 15.5615 120.0000 1.347 0.180367
## PeriodST AG 9.3375 15.5615 120.0000 0.600 0.549613
## PeriodST AG ANT 10.6250 15.5615 120.0000 0.683 0.496066
## PeriodST AG DY ANT 32.2125 15.5615 120.0000 2.070 0.040597 *
## PeriodST ANT 25.7250 15.5615 120.0000 1.653 0.100922
## Groupuntrained 8.7443 9.7792 13.0000 0.894 0.387484
## BF 0.5311 0.8137 13.0000 0.653 0.525316
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.333
## PerdDYAGANT -0.333 0.500
## PrDYAGSTANT -0.333 0.500 0.500
## PeriodDYANT -0.333 0.500 0.500 0.500
## PeriodST AG -0.333 0.500 0.500 0.500 0.500
## PerdSTAGANT -0.333 0.500 0.500 0.500 0.500 0.500
## PrSTAGDYANT -0.333 0.500 0.500 0.500 0.500 0.500 0.500
## PeriodSTANT -0.333 0.500 0.500 0.500 0.500 0.500 0.500 0.500
## Groupuntrnd -0.047 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## BF -0.847 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Grpntr
## PeriodDY AG
## PerdDYAGANT
## PrDYAGSTANT
## PeriodDYANT
## PeriodST AG
## PerdSTAGANT
## PrSTAGDYANT
## PeriodSTANT
## Groupuntrnd
## BF -0.184
# AIC and BIC values
aic_val <- AIC(avgpowerKET_FULL_MODEL)
bic_val <- BIC(avgpowerKET_FULL_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: 1454.206
cat("BIC:", bic_val, "\n")
## BIC: 1492.814
ratioKET_FULL_MODEL <- lmer(AGANT_Ratio_R_B ~ Period + Group + BF + (1 | ID),
data = biodex_data)
summary(ratioKET_FULL_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: AGANT_Ratio_R_B ~ Period + Group + BF + (1 | ID)
## Data: biodex_data
##
## REML criterion at convergence: 1040.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8662 -0.4459 0.0015 0.4309 3.8471
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 62.44 7.902
## Residual 91.49 9.565
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 46.47661 9.53353 14.58015 4.875 0.000219 ***
## PeriodDY AG -0.94750 3.38169 120.00000 -0.280 0.779818
## PeriodDY AG ANT 1.48000 3.38169 120.00000 0.438 0.662426
## PeriodDY AG ST ANT -0.49687 3.38169 120.00000 -0.147 0.883433
## PeriodDY ANT 0.97563 3.38169 120.00000 0.289 0.773460
## PeriodST AG 2.54688 3.38169 120.00000 0.753 0.452843
## PeriodST AG ANT -1.11375 3.38169 120.00000 -0.329 0.742468
## PeriodST AG DY ANT 2.15375 3.38169 120.00000 0.637 0.525413
## PeriodST ANT 5.71750 3.38169 120.00000 1.691 0.093486 .
## Groupuntrained 2.19376 4.33444 13.00000 0.506 0.621244
## BF -0.03528 0.36066 13.00000 -0.098 0.923559
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.177
## PerdDYAGANT -0.177 0.500
## PrDYAGSTANT -0.177 0.500 0.500
## PeriodDYANT -0.177 0.500 0.500 0.500
## PeriodST AG -0.177 0.500 0.500 0.500 0.500
## PerdSTAGANT -0.177 0.500 0.500 0.500 0.500 0.500
## PrSTAGDYANT -0.177 0.500 0.500 0.500 0.500 0.500 0.500
## PeriodSTANT -0.177 0.500 0.500 0.500 0.500 0.500 0.500 0.500
## Groupuntrnd -0.050 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## BF -0.919 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Grpntr
## PeriodDY AG
## PerdDYAGANT
## PrDYAGSTANT
## PeriodDYANT
## PeriodST AG
## PerdSTAGANT
## PrSTAGDYANT
## PeriodSTANT
## Groupuntrnd
## BF -0.184
# AIC and BIC values
aic_val <- AIC(ratioKET_FULL_MODEL)
bic_val <- BIC(ratioKET_FULL_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: 1066.709
cat("BIC:", bic_val, "\n")
## BIC: 1105.316
JH_Group_MODEL <- lmer(JH_cm ~ Group * Period + (1 | ID), data = jump_data)
summary(JH_Group_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: JH_cm ~ Group * Period + (1 | ID)
## Data: jump_data
##
## REML criterion at convergence: 706.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3704 -0.4794 -0.0185 0.4741 3.8970
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 8.872 2.979
## Residual 9.199 3.033
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3.413e+01 1.503e+00 4.303e+01 22.705
## GroupUntrained -8.250e+00 2.126e+00 4.303e+01 -3.881
## PeriodDY AG 1.250e-01 1.517e+00 1.120e+02 0.082
## PeriodDY AG ANT 7.500e-01 1.517e+00 1.120e+02 0.495
## PeriodDY AG ST ANT 2.250e+00 1.517e+00 1.120e+02 1.484
## PeriodDY ANT -1.975e-13 1.517e+00 1.120e+02 0.000
## PeriodST AG -1.250e-01 1.517e+00 1.120e+02 -0.082
## PeriodST AG ANT -2.500e-01 1.517e+00 1.120e+02 -0.165
## PeriodST AG DY ANT 1.250e-01 1.517e+00 1.120e+02 0.082
## PeriodST ANT 1.500e+00 1.517e+00 1.120e+02 0.989
## GroupUntrained:PeriodDY AG 1.875e+00 2.145e+00 1.120e+02 0.874
## GroupUntrained:PeriodDY AG ANT 3.000e+00 2.145e+00 1.120e+02 1.399
## GroupUntrained:PeriodDY AG ST ANT 6.250e-01 2.145e+00 1.120e+02 0.291
## GroupUntrained:PeriodDY ANT 2.000e+00 2.145e+00 1.120e+02 0.933
## GroupUntrained:PeriodST AG 1.000e+00 2.145e+00 1.120e+02 0.466
## GroupUntrained:PeriodST AG ANT 2.125e+00 2.145e+00 1.120e+02 0.991
## GroupUntrained:PeriodST AG DY ANT 1.625e+00 2.145e+00 1.120e+02 0.758
## GroupUntrained:PeriodST ANT 1.000e+00 2.145e+00 1.120e+02 0.466
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## GroupUntrained 0.000352 ***
## PeriodDY AG 0.934456
## PeriodDY AG ANT 0.621886
## PeriodDY AG ST ANT 0.140709
## PeriodDY ANT 1.000000
## PeriodST AG 0.934456
## PeriodST AG ANT 0.869359
## PeriodST AG DY ANT 0.934456
## PeriodST ANT 0.324745
## GroupUntrained:PeriodDY AG 0.383852
## GroupUntrained:PeriodDY AG ANT 0.164635
## GroupUntrained:PeriodDY AG ST ANT 0.771271
## GroupUntrained:PeriodDY ANT 0.353066
## GroupUntrained:PeriodST AG 0.641930
## GroupUntrained:PeriodST AG ANT 0.323910
## GroupUntrained:PeriodST AG DY ANT 0.450231
## GroupUntrained:PeriodST ANT 0.641930
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation matrix not shown by default, as p = 18 > 12.
## Use print(x, correlation=TRUE) or
## vcov(x) if you need it
# AIC and BIC values
aic_val <- AIC(JH_Group_MODEL)
bic_val <- BIC(JH_Group_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: 746.3944
cat("BIC:", bic_val, "\n")
## BIC: 805.7907
JH_OPT_MODEL <- lmer(JH_cm ~ Period + BF + Weight + (1 + Depth_cm| ID), data = jump_data)
summary(JH_OPT_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: JH_cm ~ Period + BF + Weight + (1 + Depth_cm | ID)
## Data: jump_data
##
## REML criterion at convergence: 734.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0600 -0.4814 -0.0121 0.4912 3.7058
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## ID (Intercept) 161.6899 12.7157
## Depth_cm 0.2635 0.5133 -0.99
## Residual 7.3301 2.7074
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 29.82276 3.37544 6.72742 8.835 6.08e-05 ***
## PeriodDY AG 1.01561 0.97105 111.89782 1.046 0.2979
## PeriodDY AG ANT 2.03852 0.98993 111.47666 2.059 0.0418 *
## PeriodDY AG ST ANT 1.57739 1.00723 113.52988 1.566 0.1201
## PeriodDY ANT 0.64131 0.97645 114.60066 0.657 0.5126
## PeriodST AG 0.33493 0.97605 113.85160 0.343 0.7321
## PeriodST AG ANT 0.40290 0.97049 112.70082 0.415 0.6788
## PeriodST AG DY ANT 0.44793 0.97613 113.62907 0.459 0.6472
## PeriodST ANT 2.02325 0.98382 115.69261 2.057 0.0420 *
## BF -0.30885 0.17897 9.67892 -1.726 0.1161
## Weight 0.08598 0.05963 9.28322 1.442 0.1822
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.145
## PerdDYAGANT -0.175 0.507
## PrDYAGSTANT -0.179 0.502 0.529
## PeriodDYANT -0.141 0.507 0.509 0.510
## PeriodST AG -0.126 0.510 0.507 0.503 0.514
## PerdSTAGANT -0.116 0.499 0.508 0.504 0.499 0.497
## PrSTAGDYANT -0.137 0.502 0.499 0.496 0.503 0.508 0.496
## PeriodSTANT -0.133 0.504 0.507 0.501 0.513 0.512 0.496 0.507
## BF -0.199 -0.004 -0.049 -0.072 0.004 0.015 -0.074 -0.037 -0.024
## Weight -0.451 0.012 0.078 0.104 0.002 -0.018 0.056 0.034 0.022
## BF
## PeriodDY AG
## PerdDYAGANT
## PrDYAGSTANT
## PeriodDYANT
## PeriodST AG
## PerdSTAGANT
## PrSTAGDYANT
## PeriodSTANT
## BF
## Weight -0.767
# AIC and BIC values
aic_val <- AIC(JH_OPT_MODEL)
bic_val <- BIC(JH_OPT_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: 764.1869
cat("BIC:", bic_val, "\n")
## BIC: 808.7341
The model diagnostics seems to show that data meets all model assumptions
check_model(JH_OPT_MODEL)
plot_model(JH_OPT_MODEL, title = "Vertical Jump Height",
show.intercept = TRUE, show.values = TRUE, digits = 3, value.offset = 0.2) +
theme_prism()
Extract coefficients and Create predictions plots
In this plot the jitter dots are the observed values with the predicted values from the LMM in the geom_lines for each participant
model_coefs <- coef(JH_OPT_MODEL)$ID %>%
rename(Intercept = `(Intercept)`) %>%
rownames_to_column("ID") %>%
mutate(ID = as.factor(ID))
merged_data <- left_join(jump_data, model_coefs, by = c("ID", "Weight", "BF", "Depth_cm"))
merged_data$predicted_jump <- predict(JH_OPT_MODEL, newdata = merged_data)
p_JH_ID <- ggplot(merged_data, aes(x = Period, y = JH_cm, group = ID, color = ID)) +
geom_jitter(size=0.1) + labs(x= "Stretching Type",y="Height (cm)",
title= "Jump Height Individual Responses") +
geom_line(aes(y = predicted_jump)) +
theme_prism() +
theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))+
guides(color = FALSE) # This line removes the color legend for ID
p_JH_ID
Plot model estimates
# Predict overall estimates without considering the random effects
overall_predictions <- predict(JH_OPT_MODEL, newdata = jump_data, re.form = NA)
jump_data$overall_predictions <- overall_predictions
# Aggregate the predictions
jump_data_agg <- jump_data %>%
group_by(Period) %>%
summarise(mean_prediction = mean(overall_predictions, na.rm = TRUE))
jump_data$Group <- factor(jump_data$Group, levels = sort(unique(jump_data$Group)))
p_JH_box <- jump_data %>%
ggboxplot(x="Period", y="JH_cm",color="Period", add="jitter",
xlab = "Stretching Type", ylab = "Height (cm)", title = "Vertical Jump Height") +
geom_point(data=jump_data_agg, aes(y=mean_prediction), color="red", size=3) + # Adding the aggregated model's estimates
geom_line(data=jump_data_agg, aes(y=mean_prediction, group=1), color="red", size=1) +
theme_prism() +
guides(color = FALSE)+
theme(axis.text.x = element_text(angle = 45, hjust = 1, vjust = 1))
p_JH_box
ggarrange(p_PTKE_box,p_PTKE_ID,p_JH_box,p_JH_ID)
ggsave("Torque_JH.png")
## Saving 11 x 10 in image
RSImod_OPT_MODEL <- lmer(RSI_mod ~ Group + Period + BF + Weight +Depth_cm + (1 + Depth_cm | ID), data = jump_data)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues
## Warning: Model failed to converge with 1 negative eigenvalue: -1.1e+00
summary(RSImod_OPT_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: RSI_mod ~ Group + Period + BF + Weight + Depth_cm + (1 + Depth_cm |
## ID)
## Data: jump_data
##
## REML criterion at convergence: 142.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1299 -0.4976 -0.1045 0.3414 5.0312
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## ID (Intercept) 1.573e-05 0.003966
## Depth_cm 1.659e-04 0.012881 -0.63
## Residual 8.956e-02 0.299262
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.468857 0.454506 9.844051 1.032 0.326949
## GroupUntrained 0.433052 0.179238 7.065416 2.416 0.046041 *
## PeriodDY AG -0.125452 0.106193 118.407166 -1.181 0.239829
## PeriodDY AG ANT -0.301816 0.106947 119.870936 -2.822 0.005587 **
## PeriodDY AG ST ANT -0.248867 0.109480 121.539996 -2.273 0.024771 *
## PeriodDY ANT -0.086719 0.106602 119.173309 -0.813 0.417562
## PeriodST AG -0.118174 0.106214 118.382603 -1.113 0.268133
## PeriodST AG ANT -0.124406 0.105910 117.774239 -1.175 0.242509
## PeriodST AG DY ANT -0.015773 0.107096 119.759983 -0.147 0.883159
## PeriodST ANT -0.226123 0.106209 118.252485 -2.129 0.035326 *
## BF 0.002982 0.020034 6.616414 0.149 0.886094
## Weight 0.003761 0.006517 5.308064 0.577 0.587474
## Depth_cm 0.033989 0.009065 45.336062 3.749 0.000501 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation matrix not shown by default, as p = 13 > 12.
## Use print(x, correlation=TRUE) or
## vcov(x) if you need it
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues
# AIC and BIC values
aic_val <- AIC(RSImod_OPT_MODEL)
bic_val <- BIC(RSImod_OPT_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: 176.5005
cat("BIC:", bic_val, "\n")
## BIC: 226.9873
Impulse_OPT_MODEL <- lmer(Relative_net_impulse ~ Period + BF + Weight + Depth_cm + (1 + Depth_cm| ID), data = jump_data)
## boundary (singular) fit: see help('isSingular')
summary(Impulse_OPT_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Relative_net_impulse ~ Period + BF + Weight + Depth_cm + (1 +
## Depth_cm | ID)
## Data: jump_data
##
## REML criterion at convergence: -61.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8001 -0.5075 -0.1722 0.2720 5.9999
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## ID (Intercept) 1.962e-02 0.140089
## Depth_cm 5.741e-05 0.007577 -1.00
## Residual 2.154e-02 0.146782
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.376408 0.116639 30.735494 3.227 0.002967 **
## PeriodDY AG 0.003520 0.052030 120.370145 0.068 0.946174
## PeriodDY AG ANT -0.034345 0.052205 120.562994 -0.658 0.511869
## PeriodDY AG ST ANT -0.022749 0.052654 121.338816 -0.432 0.666474
## PeriodDY ANT 0.053374 0.052108 120.827567 1.024 0.307736
## PeriodST AG -0.026650 0.052067 120.876215 -0.512 0.609698
## PeriodST AG ANT 0.005221 0.051984 120.429834 0.100 0.920168
## PeriodST AG DY ANT -0.005941 0.052183 120.938262 -0.114 0.909541
## PeriodST ANT -0.046175 0.052070 120.669813 -0.887 0.376958
## BF 0.002933 0.004618 46.496772 0.635 0.528518
## Weight 0.003784 0.001553 80.434488 2.437 0.017024 *
## Depth_cm 0.012098 0.002959 18.419307 4.088 0.000662 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.212
## PerdDYAGANT -0.213 0.502
## PrDYAGSTANT -0.186 0.499 0.505
## PeriodDYANT -0.199 0.502 0.502 0.502
## PeriodST AG -0.205 0.502 0.501 0.498 0.503
## PerdSTAGANT -0.203 0.500 0.500 0.497 0.499 0.499
## PrSTAGDYANT -0.207 0.500 0.499 0.497 0.500 0.501 0.497
## PeriodSTANT -0.210 0.501 0.501 0.496 0.501 0.502 0.499 0.501
## BF -0.423 -0.018 -0.023 -0.035 -0.021 -0.020 -0.027 -0.036 -0.028
## Weight -0.285 0.026 0.049 0.066 0.024 0.017 0.013 0.046 0.028
## Depth_cm -0.296 -0.028 -0.058 -0.107 -0.042 -0.023 -0.007 -0.049 -0.022
## BF Weight
## PeriodDY AG
## PerdDYAGANT
## PrDYAGSTANT
## PeriodDYANT
## PeriodST AG
## PerdSTAGANT
## PrSTAGDYANT
## PeriodSTANT
## BF
## Weight -0.586
## Depth_cm 0.122 -0.366
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# AIC and BIC values
aic_val <- AIC(Impulse_OPT_MODEL)
bic_val <- BIC(Impulse_OPT_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: -29.30643
cat("BIC:", bic_val, "\n")
## BIC: 18.21058
PF_OPT_MODEL <- lmer(Jump_time ~ Period + BF + Weight + Depth_cm + (1 + Depth_cm| ID), data = jump_data)
## boundary (singular) fit: see help('isSingular')
summary(PF_OPT_MODEL)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Jump_time ~ Period + BF + Weight + Depth_cm + (1 + Depth_cm | ID)
## Data: jump_data
##
## REML criterion at convergence: -215.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.2556 -0.6041 -0.2001 0.2627 4.7141
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## ID (Intercept) 2.439e-03 0.049385
## Depth_cm 4.901e-06 0.002214 -1.00
## Residual 7.337e-03 0.085656
## Number of obs: 144, groups: ID, 16
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.338e-02 5.013e-02 3.736e+01 1.663 0.1046
## PeriodDY AG 5.000e-03 3.034e-02 1.243e+02 0.165 0.8694
## PeriodDY AG ANT -3.276e-02 3.044e-02 1.249e+02 -1.076 0.2839
## PeriodDY AG ST ANT -1.667e-02 3.065e-02 1.253e+02 -0.544 0.5875
## PeriodDY ANT 1.184e-02 3.036e-02 1.244e+02 0.390 0.6972
## PeriodST AG -8.176e-03 3.034e-02 1.245e+02 -0.269 0.7880
## PeriodST AG ANT 1.190e-02 3.032e-02 1.243e+02 0.393 0.6953
## PeriodST AG DY ANT -1.286e-02 3.038e-02 1.245e+02 -0.423 0.6729
## PeriodST ANT -2.182e-02 3.035e-02 1.247e+02 -0.719 0.4736
## BF 3.926e-03 2.069e-03 3.579e+01 1.898 0.0659 .
## Weight 3.961e-04 7.557e-04 3.592e+01 0.524 0.6034
## Depth_cm -5.797e-05 1.281e-03 1.379e+01 -0.045 0.9645
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PrDYAG PDYAGA PDYASA PDYANT PrSTAG PSTAGA PSTADA PSTANT
## PeriodDY AG -0.288
## PerdDYAGANT -0.279 0.502
## PrDYAGSTANT -0.258 0.500 0.506
## PeriodDYANT -0.283 0.502 0.502 0.502
## PeriodST AG -0.287 0.501 0.501 0.500 0.502
## PerdSTAGANT -0.289 0.500 0.501 0.499 0.500 0.500
## PrSTAGDYANT -0.281 0.501 0.501 0.501 0.501 0.501 0.500
## PeriodSTANT -0.291 0.501 0.501 0.499 0.501 0.501 0.500 0.501
## BF -0.305 -0.014 -0.030 -0.049 -0.016 -0.011 -0.020 -0.024 -0.015
## Weight -0.197 0.021 0.047 0.077 0.026 0.015 0.018 0.033 0.022
## Depth_cm -0.368 -0.036 -0.070 -0.125 -0.048 -0.031 -0.021 -0.055 -0.031
## BF Weight
## PeriodDY AG
## PerdDYAGANT
## PrDYAGSTANT
## PeriodDYANT
## PeriodST AG
## PerdSTAGANT
## PrSTAGDYANT
## PeriodSTANT
## BF
## Weight -0.726
## Depth_cm 0.270 -0.461
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')
# AIC and BIC values
aic_val <- AIC(PF_OPT_MODEL)
bic_val <- BIC(PF_OPT_MODEL)
cat("AIC:", aic_val, "\n")
## AIC: -183.927
cat("BIC:", bic_val, "\n")
## BIC: -136.41
tab_model(PKET_FULL_MODEL,avgKET_FULL_MODEL,avgpowerKET_FULL_MODEL,
dv.labels = c("Peak Torque Knee Extension (N-m/bw)", "Average Torque Knee Extension (N-m)",
"Average Power Knee Extension (Watts)"),
show.reflvl = T, show.intercept = T, p.style = "numeric_stars", collapse.ci = TRUE)
| Peak Torque Knee Extension (N-m/bw) | Average Torque Knee Extension (N-m) | Average Power Knee Extension (Watts) | ||||
|---|---|---|---|---|---|---|
| Predictors | Estimates | p | Estimates | p | Estimates | p |
| (Intercept) |
331.09 *** (228.29 – 433.89) |
<0.001 |
122.69 *** (56.02 – 189.36) |
<0.001 |
102.64 *** (56.48 – 148.80) |
<0.001 |
| BF |
-3.86 (-7.80 – 0.08) |
0.055 |
1.80 (-0.72 – 4.32) |
0.160 |
0.53 (-1.08 – 2.14) |
0.515 |
| trained | Reference | Reference | Reference | |||
| untrained |
0.84 (-46.52 – 48.19) |
0.972 |
-1.82 (-32.10 – 28.45) |
0.905 |
8.74 (-10.60 – 28.09) |
0.373 |
| PeriodDY AG |
36.22 ** (9.12 – 63.32) |
0.009 |
20.89 (-3.25 – 45.03) |
0.089 |
20.00 (-10.78 – 50.78) |
0.201 |
| PeriodDY AG ANT |
42.12 ** (15.03 – 69.22) |
0.003 |
37.71 ** (13.57 – 61.85) |
0.002 |
33.57 * (2.78 – 64.35) |
0.033 |
| PeriodDY AG ST ANT |
51.69 *** (24.59 – 78.79) |
<0.001 |
50.29 *** (26.15 – 74.43) |
<0.001 |
40.31 * (9.53 – 71.10) |
0.011 |
| PeriodDY ANT |
26.89 (-0.21 – 53.99) |
0.052 |
23.55 (-0.59 – 47.69) |
0.056 |
20.97 (-9.82 – 51.75) |
0.180 |
| PeriodST AG |
4.15 (-22.95 – 31.25) |
0.762 |
13.20 (-10.94 – 37.34) |
0.281 |
9.34 (-21.45 – 40.12) |
0.550 |
| PeriodST AG ANT |
19.22 (-7.88 – 46.32) |
0.163 |
20.68 (-3.46 – 44.82) |
0.092 |
10.62 (-20.16 – 41.41) |
0.496 |
| PeriodST AG DY ANT |
19.29 (-7.81 – 46.39) |
0.162 |
9.43 (-14.71 – 33.57) |
0.441 |
32.21 * (1.43 – 63.00) |
0.040 |
| PeriodST ANT |
33.11 * (6.01 – 60.21) |
0.017 |
28.84 * (4.70 – 52.98) |
0.020 |
25.72 (-5.06 – 56.51) |
0.101 |
| Random Effects | ||||||
| σ2 | 1501.28 | 1191.19 | 1937.29 | |||
| τ00 | 2047.64 ID | 772.78 ID | 154.31 ID | |||
| ICC | 0.58 | 0.39 | 0.07 | |||
| N | 16 ID | 16 ID | 16 ID | |||
| Observations | 144 | 144 | 144 | |||
| Marginal R2 / Conditional R2 | 0.183 / 0.655 | 0.139 / 0.478 | 0.082 / 0.150 | |||
|
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tab_model(JH_OPT_MODEL,Impulse_OPT_MODEL,
dv.labels = c("Jump Height (cm)", "Relative Net Impulse (N-s/bw)"),
show.reflvl = T, show.intercept = T, p.style = "numeric_stars", collapse.ci = TRUE)
| Jump Height (cm) | Relative Net Impulse (N-s/bw) | |||
|---|---|---|---|---|
| Predictors | Estimates | p | Estimates | p |
| (Intercept) |
29.82 *** (23.14 – 36.50) |
<0.001 |
0.38 ** (0.15 – 0.61) |
0.002 |
| BF |
-0.31 (-0.66 – 0.05) |
0.087 |
0.00 (-0.01 – 0.01) |
0.527 |
| Depth_cm |
0.01 *** (0.01 – 0.02) |
<0.001 | ||
| PeriodDY AG |
1.02 (-0.91 – 2.94) |
0.298 |
0.00 (-0.10 – 0.11) |
0.946 |
| PeriodDY AG ANT |
2.04 * (0.08 – 4.00) |
0.041 |
-0.03 (-0.14 – 0.07) |
0.512 |
| PeriodDY AG ST ANT |
1.58 (-0.42 – 3.57) |
0.120 |
-0.02 (-0.13 – 0.08) |
0.666 |
| PeriodDY ANT |
0.64 (-1.29 – 2.57) |
0.512 |
0.05 (-0.05 – 0.16) |
0.308 |
| PeriodST AG |
0.33 (-1.60 – 2.27) |
0.732 |
-0.03 (-0.13 – 0.08) |
0.610 |
| PeriodST AG ANT |
0.40 (-1.52 – 2.32) |
0.679 |
0.01 (-0.10 – 0.11) |
0.920 |
| PeriodST AG DY ANT |
0.45 (-1.48 – 2.38) |
0.647 |
-0.01 (-0.11 – 0.10) |
0.910 |
| PeriodST ANT |
2.02 * (0.08 – 3.97) |
0.042 |
-0.05 (-0.15 – 0.06) |
0.377 |
| Weight |
0.09 (-0.03 – 0.20) |
0.152 |
0.00 * (0.00 – 0.01) |
0.016 |
| Random Effects | ||||
| σ2 | 7.33 | 0.02 | ||
| τ00 | 161.69 ID | 0.02 ID | ||
| τ11 | 0.26 ID.Depth_cm | 0.00 ID.Depth_cm | ||
| ρ01 | -0.99 ID | -1.00 ID | ||
| ICC | 0.96 | 0.32 | ||
| N | 16 ID | 16 ID | ||
| Observations | 144 | 144 | ||
| Marginal R2 / Conditional R2 | 0.014 / 0.957 | 0.429 / 0.613 | ||
|
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